Question

You just turned 35 and have been saving for an around-the-world vacation. You want to take the trip to celebrate your 40th birthday. You have set aside, as of today, $15,000 for such a trip. You expect the trip will cost $25,000. The financial instruments you have invested the $15,000 in have been earning, on average, about 8%. (You may ignore income taxes). (a) Will you have enough money in that vacation account on your 40th birthday to take the trip? What will be the surplus or shortfall in that account when you turn 40? (b) If you had to, you could further fund the trip by making, starting today, five annual $500 contributions to the account. If you adhere to such a plan, how much will be in the account on your 40th birthday?

Answer 1

Answer:

(a) No, there is a Shortfall = $2,965

(b) $25,202.95

Explanation:

As provided current balance: $15,000

Current return on investment = 8%

Assumed this is compound interest as no amount is withdrawn in between.

Therefore, future value of $1 after 5 years @ 8% compounded per year =

1.469

Value of $15,000 on the date of 40th Birthday = $15,000 $\times$ 1.469 = $22,035

There is a shortfall in the budgeted amount = $25,000 - $22,035 = $2,965

If $500 annual contributions are made in the same account then value shall be:

Value of $15,000 = $22,035

Value of $500 = Value of $1 after 5 years = $6.3359

= $500 $\times$ 6.3359 = $3,167.95

Then total balance in account = $22,035 + $3,167.95 = $25,202.95